Method and apparatus for teaching mathematics in different number systems

ABSTRACT

A method and apparatus for teaching relationships between the calculations in different number bases using a simple computer unit. The unit has a manually operable decimal input dial, manually operable binary input switches, an electrical counting circuit activated by the manual input devices, binary output indicators including a series of indicator lamps corresponding to the capacity of the counting circuit, but no memory. Interchangeable indicia strips can be placed in conjunction with the indicator lamps with indicia expressing the binary output in terms of its decimal, exponential or other equivalent. Remote dial input and large display light attachments facilitate classroom instruction. A modification of the unit has a built-in tape cassette playback component including speaker and controls for playing instructional tapes as the student learns to use the machine.

United States Patent Heath [54] METHOD AND APPARATUS FOR TEACHINGMATHEMATICS IN DIFFERENT NUMBER SYSTEMS [72] Inventor: James L. Heath,1500 Northwest 13th Street, Corvallis, Oreg. 97330 [22] Filed: June1,1970

[21] Appl.No.: 41,846

US. Cl. ..35/30, 235/155 ..G09b 19/02 Field oi Search ..35/30, 31 R, 31C, 32; 235/155, 169, 92 CV, 92 VA, 92 BN, 92 BD, 92 BQ [56] ReferencesCited UNITED STATES PATENTS 51 May 9,1972

3,245,156 I 4/1966 De Bloois et al ..35/8 R Primary Examiner-Wm. H.Grieb Attorney-Buckhorn, Blore, Klarquist and Sparkman [57] ABSTRACT Amethod and apparatus for teaching relationships between the calculationsin different number bases using a simple computer unit. The unit has amanually operable decimal input dial, manually operable binary inputswitches, an electrical counting circuit activated by the manual inputdevices, binary output indicators including a series of indicator lampscorresponding to the capacity of the counting circuit. but no memory.interchangeable indicia strips can be placed in conjunction with theindicator lamps with indicia expressing the binary output in terms ofits decimal, exponential or other equivalent. Remote dial input andlarge display light attachments facilitate classroom instruction. Amodification of the unit has a built-in tape cassette playback componentinthe student learns to use the machine.

13 Claims, 10 Drawing Figures PKTENTEBMAY 91972 SHEET 1 [1F 3 JAMES L.HEATH INVENTOR BUCKHORN, BLORE, KLARQUIST & SPARKMAN ATTORNEYSPATENTEDMAY 9 I972 I 3.660.913

SHEET 2 BF 3 FIG 6 JAMES L. HEATH v INVENTOR BY BUCKHORN, BLORE,KLARQUIST & SPARKMAN ATTORNEYS METHOD AND APPARATUS FOR TEACHINGMATHEMATICS IN DIFFERENT NUMBER SYSTEMS BACKGROUND OF THE INVENTION 1.Field of the Invention The present invention relates to the teaching ofmathematics, and more particularly to a method and apparatus forteaching mathematical concepts and relationships in different numbersystems and the relationships between such systems.

2. Description of the Prior Art Numerous mechanically and electricallyoperated devices have been suggested heretofore for teaching studentshow to calculate in different number systems. However, prior devices ofthis sort require the user to work in only a single number base, forexample, by providing a binary input sothat the device will perform abinary calculation and provide a binary output. Such prior devices donot help a student learn the relationship between different numbersystems. For example, no known prior device enable a student to workwith input or problems expressed in a familiar number base, for examplethe base 10, but with outputs or answers expressed in a different,perhaps unfamiliar number base, with means for helping the studentexpress the output in either number base.

Moreover, no known device of the aforementioned type is adaptable foruse in both large classroom situations and individual student practiceand self-teaching situations.

With the widespread adoption of the computer in education, business andindustry, and the consequential introduction of the new math in ourschool systems, there is a great need for a tool which will help bothteachers and students understand mathematical concepts underlying thenew math and computer technology.

SUMMARY OF THE INVENTION In accordance with the present invention, thedeficiencies of the prior art are overcome by providing a method andapparatus whereby a student can express a number or problem in terms ofa known number base, input the number or problem in the known numberbase into a computer and have the computer provide a visual outputexpressed in a different number base so that a student, using his mentalprocesses, can compare relationships between different number bases.

In another aspect of the invention, the operator has a choice of workingwith a decimal or binary input, in either case with the computerrendering a binary output.

Another feature of the invention is the provision of multipleinterchangeable indicia strips used in conjunction with the binaryoutput indicators to enable the user to work with number systems otherthan the binary and decimal systems.

In a further aspect of the invention, the input is discernible to thetactile, visual and auditory senses of the user, thereby enhancing thelearning process.

Another feature of the invention includes a remote input device whichcan be connected to the basic computer unit so that the basic unit canbe placed in a readily observable position at the front of a classroomwhile various students input problems into the computer using the remoteinput attachment.

Still another feature of the invention is a large light displayattachment which can be used in large classroom situations as anoverhead display output unit readily observable by all students whileindividual students manipulate the input devices of the computer.

In another aspect of the invention, two or more individual computerunits can be connected in series to multiply the capacities of theindividual units.

In still another aspect of the invention, a cassette tape playbackcomponent is incorporated in the basic computer unit for playinginstructional tapes-on the use of the machine thereby facilitating thelearning process.

Primary objects of the invention are to provide a method andapparatuswhich:

I. help the student develop a clear understanding of variousmathematical concepts including sets, numeration, addition, subtraction,multiplication and division;

2. help the student to apply various mathematical concepts in differentnumber systems;

.3. help the student learn mathematical concepts in a way that isinteresting and fun;

4. help the student learn mathematical concepts rapidly;

5. help the student gain a working knowledge of different numbersystems, the relationship between different number systems, and theability to calculate in different number systems;

6. help the student understand the operation of a simple computer;

7. help very young students learn basic mathematical concepts; and

8. enable students to set up and compare mathematical expressions,problems and solutions in different number bases.

The foregoing and other objects, features and advantages of theinvention will become more apparent from the following detaileddescription which proceeds with reference to the accompanying drawingswherein:

FIG. 1 is a front perspective view of a computer in accordance with theinvention;

FIG. 2 is a remote dial input extension attachment for'use with theapparatus of FIG. I;

FIGS. 3a, 3b and 3c are front views of output indicia strips for use inconjunction with the apparatus of FIG. 1;

FIG. 4 is a back view of the apparatus of FIG. I on a reduced scale;

FIG. 5 is a circuit diagram of the counting circuit within the apparatusof FIG. 1;

FIG. 6 is a front perspective view of an overhead light dis I DETAILEDDESCRIPTION GENERAL ASSEMBLY With reference to the drawings, FIG. Ishows the basic computer unit in accordance with the invention includinga housing 10 which may be made of a molded plastic or any other suitablematerial having the necessary strength, rigidity and durability. Thehousing may be given anattractive coloration to appeal to youngstudents. A front face of the housing includes a control panel 12.

An electrical counting circuit means 14, shown in FIG. 5, is installedwithin housing 10 and may be incorporated in a printed circuit board(not shown). The counting circuit comprises a series of six bistablemultivibrator circuits, or so-called flip-flop circuits, 16a, 16b, 16c,16d, 16, 16f, connected in the manner shown in FIG. 5.

The electrical circuitry is mounted on a rigid metal or other suitablebase member 18, shown in FIG. 4, forming the bottom and a portion of theback of the unit and meeting the molded plastic housing 10 along theparting line 20. The outer face of the back portion of base 18 mounts acarrying handle 22, an input jack 24, an output jack 26, andaneight-prong electrical receptacle 28. A power cord 30 extends throughthe back of base 18. The foregoing electrical components are also shownin the circuit diagram of FIG. 5.

CONTROL PANEL Referring to FIGS. 1 and 5, control panel 12 includes amain power switch 32 which, when turned to its on position, illuminatesa light 34 visible through the switch button. A manually operabledecimal input dial 36 enables the user to input any decimal number asindicated into the binary counting circuit. The mechanical decimal inputrepresented by dial 36 is converted by the counting circuit means to anelectrical binary input signal at switch 38. The dial with its visibleindicia 40 expressed in the decimal number system enables the operatorto discern the size of the number being input into the computer circuitthrough his tactile, visual and auditory senses.

There is also a manually operated binary input represented by the sixthree-position switches 42a, 42b, 42c, 42d, 42e, 42f. Each such inputswitch 42 is biased to its intermediate off position and the operator,by depressing momentarily the upper or lower half of one of suchbuttons, sends a single input signal to the counting circuitcorresponding to the selected button. The counting circuit includesbinary output means recordable at six visible binary output indicatorscomprising the six lamps 44a, 44b, 44c, 44d, 44e, 44f visible on thecontrol panel in positions corresponding to the six binary inputswitches.

The counting circuit and control panel also includes a twopositionclearing switch 46 which is normally biased to its open position butwhich, when pressed closed momentarily, clears the total indicated bythe illuminated binary output indicator lights 44 by turning off suchlights.

INDICATOR STRIPS Referring to FIG. 1 and FIGS. 3a, 3b and 3c, a seriesof interchangeable indicia means in the form of indicator strips 48a,48b, 48c, 48d are provided for use in conjunction with the outputindicator lamps 44. Each strip is made of a transparent plastic materialand has a series of six square openings 50 therethrough sized and spacedto fit over the square covers of indicator lamps 44. The decimal orexponential expression for each binary output lamp is printed on eachstrip beneath the appropriate opening or series of openingscorresponding to the lamps representing such expression. For example,strip 48a has the decimal equivalent of each binary output lamp printedbeneath the appropriate opening. Thus if lamp 44f is illuminated,indicator strip 48a will indicate that the total of the binary outputexpressed in the base is 1. Similarly, if lamp 44:: is illuminated, thisindicates that the decimal equivalent ofthe binary output is 2,expressed in the base l0, and so forth.

Indicator strip 48b is designed to give the exponential expressions forthe various binary outputs expressed in the base 2. Strip 480 isdesigned to express the exponential expressions of the various outputsin the base 4. Strip 48d is designed to give the exponential expressionsof the output lamps in the base 8. Thus the indicator strips enable abeginning user of the machine to learn to work mathematical concepts inseveral different number systems, thereby enhancing the learningprocess.

REMOTE INPUT FIG. 2 shows a dial input extension attachment 52 for theunit of FIG. 1. Such attachment includes a base 54 housing the necessaryelectrical switch device for converting the manually operated decimalinput of a dial 56 to an electrical binary signal for transmission tothe input side of the counting circuit in the main unit. Dial 56 is aduplicate of the primary decimal input dial 36. The input signal fromthe remote dial input is transmitted through a power cord 58 whichincludes a male connector jack 60 designed to fit within the input jack24 on the back of the main unit. The remote dial input extension isdesigned to enable various students in a classroom to dial inputsintothe main computer unit from remote points in the classroom whilethe unitis at the front of the class where all may observe the resulting output.

LARGE LIGHT OUTPUT DISPLAY A 'large lightdisplay attachment 62 for usewith the unit of FIG. I is shown in FIG. 6. The display unit includes aseries of six lamps 64 corresponding to the output lamps on the basicunit. Remote display unit 62 carries its own series of flipflop circuits66, one of which is shown schematically in FIG. 7 for illuminating thelamps 64 of the display unit. A power cord 68 with eight-prong plug 70is designed to fit within receptacle 28 on the back of the main unit.The main unit provides the output signals necessary to energize theflip-flop circuits in the remote display unit. Thus the output of eachflip-flop circuit in the main unit is channeled through cord 68 to acorresponding flip-flop in the remote light display unit. A powertransistor 72 in conjunction with each remote flip-flop circuitenergizes each display light 64.

The remote large light display unit is designed for use in large groupinstructional situations. For example, it might be desirable for theinstructor or a student to manipulate the input devices on the main unitor on a remote input dial extension as shown in FIG. 2, with theresultant output being visible to a large number of people at a greatdistance from the display unit.

FIG. 8 MODIFICATION A modified form of the invention is shown in FIG. 8.In this modification a tape reader or playback component indicatedgenerally at 76 is incorporated in the basic computer unit similar tothe unit of FIG. 1. That is, the unit of FIG. 8 has a housing similar tothat of FIG. 1 but of a size sufficient to incorporate the additionaltape playback component. The purpose of the tape playback component isto allow instructional tapes on the use of the computer to be played bythe student as he learns how to use the unit, either in a classroomsituation or in the absence of a teacher. This feature also assistsstudents who have difficulty reading or following written instructions.

The playback unit is of the type adapted to receive a standardcommercial two-track tape cassette 80 within an opening 82 in housing78. An amplifier (not shown) is built into the unit to increase thepower of the reader signal to drive a builtin speaker 84 or a remoteearphone connected to the basic unit at an earphone jack 86. The audiosignal is, of course, carried on one track of the two-track tapeprovided in the tape cassette.

The second track of the two-track tape is used to allow the computer tocontrol the display of a 35 mm. slide projector through a slideprojector adapter socket 88. This feature allows audio instructions tocontrol visual examples of problems projected from a slide projectorthat the student will then work out on the computer. Problems can bepresented and then student responses reinforced with these audio andvisual features.

The inclined front face portion of the basic unit carries tape controlsincluding an on-off-volume control 91, a play/stop control 92 and arewind control 93.

Housing 78 also has a control panel 12a carrying the same controls asprovided in the control panel 12 of the unit shown in FIG. 1, includinga decimal input dial 36a, clearing switch 46a and main power switch 32a.

OPERATION The operation of the computer of FIG. land a suggested programfor teaching mathematical concepts using such computer are contained ina publication entitled "Educomp Mathematics, published in 1969 byEducomp, Inc., of Corvallis, Oregon, and authored by the applicant andGary Tressel.

PREPARATION FOR USE The computer is turned on by plugging in power cord70 to an electrical outlet and pressing down on the upper portion ofmain power switch 32, causing light 34 beneath the switch button toilluminate. To turn the computer off, the lower portion of the sameswitch 32 is pressed down.

If it is desired to work in the binary or base 2 system, the indiciastrip 48a containing the numbers 1, 2, 4, 8, 16,32 can be slipped overthe indicator light cases on the control panel as shown in FIG. 1 tohelp the student interpret the binary output of the computer in terms ofthe decimal system or base 10. Alternatively, the student could use theindicia strip 48b marked 2, 2, 2*, 2, 2, 2 if working in the base 2tohelp interpret the output in terms of its exponential equivalent.Similarly, if the student wishes to work in the base 4, he can use theindicia strip marked 4, 4, 4 in the same manner. If working in the base8, the student can use the indicia strip marked 8, 8 as an aid tointerpreting the value of the lights in such base.

USE OF INPUT DIAL Assuming that the student is working in the base 2 andthe indicia strip 48a is over the output lights as shown in FIG. I, thestudent may enter any decimal number into the computer by dialing suchnumber as indicated on the dial. For example, by dialing the number 1into the computer, the first light 44f to the left of the dialilluminates since such light represents the decimal number I in thebinary system. If the decimal number 2 is dialed into the computer, thesecond light 44c to the left of the dial illuminates since that singlelight represents the decimal number 2 in the binary system. If thedecimal number 3 is dialed into the computer, both lights 44f and 44 goon because such two lights, representing the numbers 2and 1, addedtogether equal 3. If the number 4 is dialed into the computer, only thethird light 44d illuminates, since that light represents the decimalnumber 4 in the binary system.

Similarly, if the number 5 is dialed into the computer, the first andthird lights illuminate. If the number 6- is dialed into the computer,the second and third lights illuminate. If the number 7 is dialed intothe computer, the first three lights illuminate, representing thedecimal number 7 in the binary system. If the number 8 is dialed intothe computer, only the fourth light 44c goes on. If the number 9 isdialed into the computer, the first and fourth lights illuminate sincethe decimal value of such lights together totals 9. If the number 10 isdialed into the computer, the second and fourth lightsilluminate.

Y The foregoing assumes that after each number is dialed into thecomputer the lights off or clearing switch 46 is pressed to clear orextinguish preceding input and indicator lights. If this is not done,two consecutive numbers dialed into the computer are added together bythe counting circuit and the sum of these numbers is indicated on theoutput indicator lights.

Thus to dial a number into the computer greater than the number 10, anycombination of numbers indicated on the dial totalling the desirednumber can be dialed in to have the indicator lights represent suchnumber. For example, the

. number II can be dialed into the computer by dialing in'the number 10and the number I consecutively without pressing the clearing switch,causing the first, second and fourth lights 44f, 44c and 440 to lightup. Alternatively, the number 1 1 can be dialed into the computer bydialing in the numbers 6 and 5, with the same result shown on the outputlights.

Similarly the number 23 can be dialed into the computer by dialing inthe number 10 twice and the number 3 once without clearing the lightsbetween dialings. This would result in the first, second, and fifthlights to the left of the dial illuminating.

If the number 63 is dialed into the computer, all six lights wouldilluminate. The decimal number 63 thus represents the capacity of theillustrated computer when working in the base 2. However, the capacitycan be multiplied, if desired, by connecting together two such computerswith a connector cable leading from the output jack of one to the inputjack of the other.

USE OF INPUT SWITCHES Numbers can also be'put into-the computer usingthe input switches 42- below the lights. The switch below each lightrepresents the same number value as the light itself. For example, toput th e;d eci m al number 1 into the computer, the first switch 42ftotheleftiof the dial: is pressed down momentarily; to enter the number 2into the computer, the second switch would be pressed once momentarily;and to enter the number 3, the first two switches would be pressedconsecutively without clearing between presses. To enter the number 4,the third switch is pressed; to enter the number 8, the fourth switch ispressed; to enter the number l6, the fifth switch is pressed; and toenter the number 32, the sixth switch is pressed.

Any number can be put into the computer by pressing any combination ofthe switches that will give that number. For example, the number 8 canbe put into the computer either by pressing the fourth switch to theleft of the dial once, or by pressing the third switch twice, or bypressing the second switch four times, without clearing the lightsbetween presses.

Each inputswitch has a normally centered or neutral position. A numberis entered into the computer either by pressing down on the upper partof the switch if the light above the switch is off, or by pressing downon the lower part of the switch it the light above the switch is alreadyon. Thus to enter the number 34 into the computer via the switchesassuming no lightsare on, the upper part of the fifth switch 44b can bepressed down and released, then the lower part of the same switch ispressed down and released without clearing the lights between presses,then the second switch Me is pressed. The second and sixth lights shouldnow be on, representing the decimal number 34 in the binary system.

Using the foregoingprocedures, the student can be readily taught toexpress base 10 numbers in the base 2 or binary .system and base 2numbers in the base 10, using the computer NUMBER SETS The computer canalso be used to help teach the theory of number sets. For example, thestudent observes thatby pressing the top of the second input switch 44once, he puts a first. set of 2 into the computer and the second lightilluminates. Then by pressing the bottom of the second switch, he puts asecond set of 2 into the computer, and the third light illuminates,indicating that two sets of the number 2 equals 4. Then by putting athird set of 2 into the computer, he learns that three sets of 2 equals6 by observing that the second and third lights are on. He also learnsthat three sets of 2 are expressed-in the binary system as 1 10 as shownby the computer indicator lights or as 6 in the decimal system by notingthe decimal equivalents of the lights on the strip 48a.

ADDITION By now it is apparent that the computer adds numbers togetherthat are put into the computer when the indicator lights are notclearedbetween inputs.1'l'hus the student readily learns to add usingthecomputer and to express the result either in the decimal or the binarysystem. For example, the student can add the numbers 7, 2 and 5 and findtheir sum by dialing such numbers consecutively into the computerwithout clearing the lights between dialings. When he does this, henotices that the second, third and fourth indicator lights areilluminated, representing a total of 14, or, expressed in the base 2,1110. Thus he soon learns to convert readily between decimal and binaryexpressions of a given number.

MULTIPLICATION By using the computer the student learns thatmultiplication is actually multiple addition. For example, he learnsthat 3 X 4 can beexpressed as three sets of 4 or four sets of 3. Helearns to find the solution either by (l) pressing the third switchrepresentingthe number 4 three times to enter three sets of 4 into thecomputer, or by (2) dialingthree sets of 4 into the computer and thenreading the solution either in the binary system as 1100, or in thedecimal system as 12. Alternatively he can put four sets of 3 into thecomputer using either the switches or dials in the same manner.

SUBTRACTION The student also learns to subtract directly using thecomputer and the theory of complements. For example, to find thesolution to the subtraction problem 9 5, the student proceeds asfollows:

1. First he dials or pressed 9 into the computer and notices whichlights are illuminated and which lights remain ofi";

2. Now he clears the lights to extinguish the first and fourth lightsthat were illuminated;

3. He turns on the second, third, fifth and sixth lights that were offby pressing the corresponding switches;

4. Now he dials 5 into the computer;

5. Now he clears the first, second, fourth, fifth and sixth lights thatare on and turns on the third light which was off by pressing the thirdswitch. This light represents the solution to the problem, being thenumber 4.

DIVISION Once the student masters subtraction using the computer, he canreadily go on to learn division. Just as multiplication can beconsidered multiple addition, he finds that division can be consideredmultiple subtraction. For example, the solution to a division problemcan be found on the computer as follows, assuming the problem is 27divided by 8:

1. First dial or press the number 27 into the computer and observe thatthe first, second, fourth and fifth lights only are illuminated;

2. Now clear the lights;

3. Illuminate the third and sixth lights that were out by pressing theappropriate switches;

4. Now dial or press the divisor number 8 into the computer;

. Dial again the number 8 into the computer a second time;

. Now dial the number 8 into the computer a third time and notice thatthe third, fourth, fifth and sixth lights are on, but the first andsecond lights are off. Since the lights that are now off represent thenumber 3, which is lower than the divisor 8, this means that the divisor8 cannot go into the number 27 any more times. Since the number 8 hasbeen put into the computer three times and the total of the lights thatare off is 3, the answer to the problem 27 8 is 3 with a remainder of 3.

The foregoing procedure is known as division with complements.

Learning the foregoing and other mathematical concepts can be greatlyfacilitated using a computer as described. Moreover, the student willfind that learning such concepts is much more interesting and fun whenthe computer is used as a tool in the process. The student soon learnsto work in different number bases and to convert from one number base toanother with ease.

The computer as described is simple and inexpensive to manufacture,light in weight, easily transportable, virtually maintenance-free andusable either in large classroom situations or by students workingalone.

A student is capable of teaching himself the various mathematicalconcepts when the computer is used in conjunction with theaforementioned Educomp Mathematics" arithmetic workbook, the tapeplayback unit, or both.

Having described what is presently a preferred embodiment of myinvention, it should be apparent to those skilled in the art that thesame permits of modification in arrangement and detail. I claim as myinvention all such modifications as come within the true spirit andscope of the following claims.

I claim:

1. Apparatus for teaching mathematics in different number basescomprising: 7

manually operable mechanical input means in a decimal number base,

electrical counting circuit means, including a series of interconnectedindividual counting circuits, and a clearing switch for clearing saidcircuits,

means for converting said mechanical input means to an electrical inputmeans for input to said electrical counting circuit means,

said counting circuit means having output means including a visualoutput totalling means expressed in a binary number base, said visualoutput totalling means including a series of lamps corresponding innumber to the number of individual counting circuits embodying saidcounting circuit means,

manually operable mechanical input means in a binary number base andmeans for converting said mechanical input means in said binary numberbase to an electrical input means in said binary base to said countingcircuit means,

said mechanical input means in said binary and decimal number basesembodying indicia means discernible to the visual, auditory and tactilesenses of the operator activating said input means.

2. Apparatus according to claim 1 wherein said decimal mechanical inputmeans comprises a rotary dial switch means having visible, audible andtactile indicia of input.

3. Apparatus according to claim 1 wherein said apparatus is embodied ina portable, desk-top-sized housing unit and said mechanical andelectrical input means include a separable input extension meansselectively attachable to said apparatus by a flexible electricalconduit means for effecting an input from a point remote from said unit.

4. Apparatus according to claim 1 including interchangeable indiciastrip meansoperable and attachable in association with and selectivelydetachable from association with said lamps, each said indicia meansincluding means translating the visual output represented by said lampsin said binary number base to an equivalent expression in another numbersystem.

5. Apparatus according to claim 1 including a portable desk-top-sizedhousing unit embodying the various said means, said counting circuitmeans including input and output connector means connected in saidcircuit means in a manner so that said input connector means of one saidhousing unit can be connected to said output connector means of anothersaid housing unit so as to connect said counting circuit means of onesaid unit in series with said counting circuit means of another saidunit, thereby to multiply the calculating capacity of said units.

6. Apparatus according to claim 1 wherein said apparatus is embodied ina first desk-top-sized housing unit including electrical receptaclemeans connected to the output side of each individual counting circuitembodying said counting circuit means, said visual output meansincluding a second unit separated from said first unit and embodyinglarge display lamp indicia in said binary number base for large groupinstruction.

7. Apparatus according to claim 6 wherein said second unit includes aseries of individual counting circuits corresponding in number to theindividual counting circuits of said first unit, and flexible electricalconductor means including an electrical connector means for matingconnection with said receptacle means to interconnect the outputs ofsaid individual circuits of said first unit with the individual circuitsof said second unit.

8. Apparatus according to claim 1 wherein said apparatus is embodied ina housing unit, said unit embodying a tape playback means including aspeaker means and control means for transmitting taped audibleinstructions to a user of said apparatus.

9. Apparatus according to claim 1 including a portable desk-top-sizedhousing containing said counting circuit means,

said housing defining a front face,

said decimal input means comprising a rotary telephone dial-type switchwith said dial positioned on said front face,

said binary input means comprising a series of three-position switchesaligned on said front face and corresponding in number to the number ofindividual counting circuits,

each said three-position switch being electrically connected to adifferent one of said counting circuits and having a first neutralposition, a second position connecting the switch to one side of itsassociated circuit, and a third position connecting the switch to theopposite side of its associated circuit,

said lamps including visible portions on said face and arranged each inassociation with a different one of said three-position switches,

each said lamp and associated said three-position switch beingelectrically connected to the same one of said counting circuits so thateach associated three-position switch and lamp represent the same binaryexpression.

10. Apparatus according to claim 9 including a series of indicia stripseach representative of a different number system, each. said striphaving a series of openings therethrough corresponding in number to thenumber of said lamps and arranged so that said strips can be selectivelyplaced over said lamps with said lamps extending through said openingsand thereby retaining said strips on said face.

11. A teaching device for teaching calculation in different number basesand for enabling the comparison of calculations in an'unfamiliar basewith the same calculations ina familiar number base, said devicecomprising:

a portable desk-top-sized housing having a front face,

electrical binary counting circuit means comprising a series ofseries-connected bistable multivibrator counting circuits eachrepresentative of a different binary number, decimal input meanscomprising a manually operable tenposition rotary telephone dial-typeswitch with automatic return and having decimal indicia on the dial facepositions, said rotary dial including said dial face being on saidhousing face, and said rotary switch being operable to transmit a numberof electrical pulses corresponding to the decimal number dialed and anaudible signal of a length corresponding to the decimal number dialed,

an electrical lead leading directly from said dial switch to a first oneof said series of counting circuits corresponding to the lowest binarynumber represented by said circuits, for transmitting said decimal dialpulses into said first circuit,

binary input means comprising a series of manually operable,three-position input switches on said housing face corresponding innumber to the number of said counting circuits,

three-position said threeswitch having a normally open position and twoclosed positions including a first closed position for transmitting asingle electrical pulse at a time through a first lead to one side ofits corresponding counting circuit and a second closed position fortransmitting a single electrical pulse at a time through a second leadto theopposite side of the same said corresponding counting circuit sothat when said first and second positions of said three-position switchare closed alternately, the associated counting circuit is operated inadditive fashion,

and a series of electrical lamps corresponding in number to the numberof counting circuits and three-position input switches, said lamps beingarranged on said housing face, each in association with one of saidthree-position switches, each said lamp being electrically connected tothe output side of a different one of said counting circuits with eachlamp and its associated said three-position switch being electricallyconnected to the same said counting circuit so that each lamp andthree-position switch represents the same binary expression,

and normally open clearing switch means operable on the outside of saidhousing and electrically connected in said counting circuit means in amanner to clear all of said multivibrator counting circuits andmultivibrator associated outputlamps when closed.

An apparatus for teaching mathematics in different number basescomprising:

manually operable decimal input means providing visual,

tactile and audible indications of a decimal input,

manually operable binary input means providing visual, tactile andaudible indications of a binary input,

an electrical binary counting circuit means for receiving input signalsfrom said decimal'and binary input means including means for convertingdecimal inputs to binary inputs, and clearing switch means for clearingsaid counting circuit means,

a visual binary output means comprising a series of indicator lamps forreceiving output signals from said counting circuit means,

and multiple interchangeable indicia strip means for use in associationwith said indicator lamps for translating said binary output asindicated by said lamps to a decimal or other equivalent thereof,

said apparatus being housed in a portable desk-top-sized housing, withsaid manual decimal and binary input means and said lamps being providedon a front face of said housing.

13. A method of teaching mathematical concepts and relationships andcalculations in different number systems comprising:

feeding visually, audibly and tactilely discernible decimal or binaryinputs into an automatic electrical binary counter,

converting each said decimal input to its binary equivalent and addingelectrically said converted input to previous binary or converteddecimal inputs using said binary counter to obtain a binary output fromsaid counter,

transmitting said binary output to visually discernible binary outputindicator lamps,

then comparing the result expressed by said lamps in the binary numbersystem with the same result expressed in the decimal number system.

* l l i i UNITED. STATES PATENT OFFICE CERTIFICATE OF CORRECTION PatentNo. 3 660 D t d y I 1972 Inventor(s) JAMES L. HEATH It is certified thaterror appears in the above-identified patent and that said LettersPatent are hereby corrected as shown below:

Column l, line- 20, "enable" should be -enables-;

Column 7, line ll, "pressed" should be --presses---; v 'Column7, line47, "27 8" should be -27 e 8--;

Column 9, line 50, claim 11, "three-position said three" should be -eachsaid thr'ee-position;

Column 10, line 19, claim 11, "multivibrator" (second occurrence) shouldbe --their.

Signed and sealed this 6th day of March 1973.

(SEAL) Attest:

EDWARD M.FLETCHER,JR. ROBERT GOTTSCHALK Attesting Officer Commissionerof Patents FORM PO-105O (10-69) USCOMM-DC GOING-P6:

b us GOVERNMENT PRINTING OFHCF I969 n-1mwa3ll UNITED STATES PATENTOFFICE CERTIFICATE OF CORRECTION Patent No. 3 I 660 I913 Dat d y 9 1972Inventor(s) JAMES L. HEATH It is certified that error appears in theabove-identified patent and that said Letters Patent are herebycorrected as shown below:

Column 1, line 20, "enable" should be -enables-;

Column 7, line ll, "pressed" should be -presses-; 'Co1umn7, line 47, "278" should be --27 8--;

Column 9, line 50, claim 11, "three-position said three" should be--each said threeposition-;

Column 10, line 19, claim 11, "multivibrator" (second occurrence) shouldbe --their-.

Signed and sealed this 6th day of March 1973.

(SEAL) Attest:

EDWARD M.FLETCHER,JR. ROBERT GOTTSCHALK Attesting Officer Commissionerof Patents FORM PO-105O (10-69) USCOMM-DC 603/04 6:

h u.s. GOVERNMENT PRINTING 0mm I969 1-'u.. ran

1. Apparatus for teaching mathematics in different number basescomprising: manually operable mechanical input means in a decimal numberbase, electrical counting circuit means, including a series ofinterconnected individual counting circuits, and a clearing switch forclearing said circuits, means for converting said mechanical input meansto an electrical input means for input to said electrical countingcircuit means, said counting circuit means having output means includinga visual output totalling means expressed in a binary number base, saidvisual output totalling means including a series of lamps correspondingin number to the number of individual counting circuits embodying saidcounting circuit means, manually operable mechanical input means in abinary number base and means for converting said mechanical input meansin said binary number base to an electrical input means in said binarybase to said counting circuit means, said mechanical input means in saidbinary and decimal number bases embodying indicia means discernible tothe visual, auditory and tactile senses of the operator activating saidinput means.
 2. Apparatus according to claim 1 wherein said decimalmechanical input means comprises a rotary dial switch means havingvisible, audible and tactile indicia of input.
 3. Apparatus according toclaim 1 wherein said apparatus is embodied in a portable, desk-top-sizedhousing unit and said mechanical and electrical input means include aseparable input extension means selectively attachable to said apparatusby a flexible electrical conduit means for effecting an input from apoint remote from said unit.
 4. Apparatus according to claim 1 includinginterchangeable indicia strip means operable and attachable inassociation with and selectively detachable from association with saidlamps, each said indicia means including means translating the visualoutput represented by said lamps in said binary number base to anequivalent expression in another number system.
 5. Apparatus accordingto claim 1 including a portable desk-top-sized housing unit embodyingthe various said means, said counting circuit means including input andoutput connector means connected in said circuit means in a manner sothat said input connector means of one said housing unit can beconnected to said output connector means of another said housing unit soas to connect said counting circuit means of one said unit in serieswith said counting circuit means of another said unit, thereby tomultiply the calculating capacity of said units. Pg,20
 6. Apparatusaccording to claim 1 wherein said apparatus is embodied in a firstdesk-top-sized housing unit including electrical receptacle meansconnected to the output side of each individual counting circuitembodying said counting circuit means, said visual output meansincluding a second unit separated from said first unit and embodyinglarge display lamp indicia in said binary number base for large groupinstruction.
 7. Apparatus according to claim 6 wherein said second unitincludes a series of individual counting circuits corresponding innumber to the individual counting circuits of said first unit, andflexible electrical conductor means including an electrical connectormeans for mating connection with said receptacle means to interconnectthe outputs of said individual circuits of said first unit with theindividual circuits of said second unit.
 8. Apparatus according to claim1 wherein said apparatus is embodied in a housing unit, said unitembodying a tape playback means including a speaker means and controlmeans for transmitting taped audible instructions to a user of saidapparatus.
 9. Apparatus according to claim 1 including a portabledesk-top-sized housing containing said counting circuit means, saidhousing defining a front face, said decimal input means comprising arotary telephone dial-type switch with said dial positioned on saidfront face, said binary input means comprising a series ofthree-position switches aligned on said front face and corresponding innumber to the number of individual counting circuits, each saidthree-position switch being electrically connected to a different one ofsaid counting circuits and having a first neutral position, a secondposition connecting the switch to one side of its associated circuit,and a third position connecting the switch to the opposite side of itsassociated circuit, said lamps including visible portions on said faceand arranged each in association with a different one of saidthree-position switches, each said lamp and associated saidthree-position switch being electrically connected to the same one ofsaid counting circuits so that each associated three-position switch andlamp represent the same binary expression.
 10. Apparatus according toclaim 9 including a series of indicia strips each representative of adifferent number system, each said strip having a series of openingstherethrough corresponding in number to the number of said lamps andarranged so that said strips can be selectively placed over said lampswith said lamps extending through said openings and thereby retainingsaid strips on said face.
 11. A teaching device for teaching calculationin different number bases and for enabling the comparison ofcalculations in an unfamiliar base with the same calculations in afamiliar number base, said device comprising: a portable desk-top-sizedhousing having a front face, electrical binary counting circuit meanscomprising a series of series-connected bistable multivibrator countingcircuits each representative of a different binary number, decimal inputmeans comprising a manually operable ten-position rotary telephonedial-type switch with automatic return and having decimal indicia on thedial face positions, said rotary dial including said dial face being onsaid housing face, and said rotary switch being operable to transmit anumber of electrical pulses corresponding to the decimal number dialedand an audible signal of a length corresponding to the decimal numberdialed, an electrical lead leading directly from said dial switch to afirst one of said series of counting circuits corresponding to thelowest binary number represented by said circuits, for transmitting saiddecimal dial pulses into said first circuit, binary input meanscomprising a series of manually operable, three-position input switcheson said housing face corresponding in number to the number of saidcounting circuits, three-posiTion said three- switch having a normallyopen position and two closed positions including a first closed positionfor transmitting a single electrical pulse at a time through a firstlead to one side of its corresponding counting circuit and a secondclosed position for transmitting a single electrical pulse at a timethrough a second lead to the opposite side of the same saidcorresponding counting circuit so that when said first and secondpositions of said three-position switch are closed alternately, theassociated counting circuit is operated in additive fashion, and aseries of electrical lamps corresponding in number to the number ofcounting circuits and three-position input switches, said lamps beingarranged on said housing face, each in association with one of saidthree-position switches, each said lamp being electrically connected tothe output side of a different one of said counting circuits with eachlamp and its associated said three-position switch being electricallyconnected to the same said counting circuit so that each lamp andthree-position switch represents the same binary expression, andnormally open clearing switch means operable on the outside of saidhousing and electrically connected in said counting circuit means in amanner to clear all of said multivibrator counting circuits andmultivibrator associated output lamps when closed.
 12. An apparatus forteaching mathematics in different number bases comprising: manuallyoperable decimal input means providing visual, tactile and audibleindications of a decimal input, manually operable binary input meansproviding visual, tactile and audible indications of a binary input, anelectrical binary counting circuit means for receiving input signalsfrom said decimal and binary input means including means for convertingdecimal inputs to binary inputs, and clearing switch means for clearingsaid counting circuit means, a visual binary output means comprising aseries of indicator lamps for receiving output signals from saidcounting circuit means, and multiple interchangeable indicia strip meansfor use in association with said indicator lamps for translating saidbinary output as indicated by said lamps to a decimal or otherequivalent thereof, said apparatus being housed in a portabledesk-top-sized housing, with said manual decimal and binary input meansand said lamps being provided on a front face of said housing.
 13. Amethod of teaching mathematical concepts and relationships andcalculations in different number systems comprising: feeding visually,audibly and tactilely discernible decimal or binary inputs into anautomatic electrical binary counter, converting each said decimal inputto its binary equivalent and adding electrically said converted input toprevious binary or converted decimal inputs using said binary counter toobtain a binary output from said counter, transmitting said binaryoutput to visually discernible binary output indicator lamps, thencomparing the result expressed by said lamps in the binary number systemwith the same result expressed in the decimal number system.